Let m,n≥3, (m−1)(n−1)+2≤p≤mn, and u=mn−p. The set Ru×n×m of all real tensors with size u×n×m is one to one corresponding to the set of bilinear maps Rm×Rn→Ru. We show that Rm×n×p has plural typical ranks p and 05f646dfd08f2612976d6" title="Click to view the MathML source">p+1 if and only if there exists a nonsingular bilinear map Rm×Rn→Ru. We show that there is a dense open subset 5e1f46241c66b6bc5a13e438fac" title="Click to view the MathML source">O of Ru×n×m such that for any Y∈O, the ideal of maximal minors of a matrix defined by Y in a certain way is a prime ideal and the real radical of that is the irrelevant maximal ideal if that is not a real prime ideal. Further, we show that there is a dense open subset e4554e20028030ccd0b9b" title="Click to view the MathML source">T of Rn×p×m and continuous surjective open maps 5ef75c9e9a5b87345635826f14262b" title="Click to view the MathML source">ν:O→Ru×p and σ:T→Ru×p, where Ru×p is the set of u×p matrices with entries in R, such that if 0592c1e0674dca256103e587b25ca5" title="Click to view the MathML source">ν(Y)=σ(T), then if and only if the ideal of maximal minors of the matrix defined by Y is a real prime ideal.